The structure and dynamical evolution of dark matter haloes

We use N-body simulations to investigate the structure and dynamical evolution of dark matter haloes in clusters of galaxies. Our sample consists of nine massive haloes from an Einstein-De Sitter universe with scale-free power spectrum and spectral index n=-1. Haloes are resolved by 20 000 particles each, on average, and have a dynamical resolution of 20-25 kpc, as shown by extensive tests. Large-scale tidal fields are included up to a scale L=150 Mpc using background particles. We find that the halo formation process can be characterized by the alternation of two dynamical configurations: a merging phase and a relaxation phase, defined by their signature on the evolution of the total mass and root mean square (rms) velocity. Haloes spend on average one- third of their evolution in the merging phase and two-thirds in the relaxation phase. Using this definition, we study the density profiles and show how they change during the halo dynamical history. In particular, we find that the average density profiles of our haloes are fitted by the Navarro, Frenk & White analytical model with an rms residual of 17 per cent between the virial radius R_v and 0.01R_v. The Hernquist analytical density profile fits the same haloes with an rms residual of 26 per cent. The trend with mass of the scale radius of these fits is marginally consistent with that found by Cole & Lacey: compared with their results our haloes are more centrally concentrated, and the relation between scale radius and halo mass is slightly steeper. We find a moderately large scatter in this relation, due both to dynamical evolution within haloes and to fluctuations in the halo population. We analyse the dynamical equilibrium of our haloes using the Jeans equation, and find that on average they are approximately in equilibrium within their virial radius. Finally, we find that the projected mass profiles of our simulated haloes are in very good agreement with the profiles of three rich galaxy clusters derived from strong and weak gravitational lensing observations.